A tree approach to \(p\)-variation and to integration

DOI10.1214/07-AOP388zbMath1157.60055arXiv0705.2128OpenAlexW2060479255MaRDI QIDQ2519682

Jean Picard

Publication date: 27 January 2009

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.2128

zbMATH Keywords

Lévy processesfractional Brownian motionLebesgue-Stieltjes integralrough path

Mathematics Subject Classification ID

Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Sample path properties (60G17) Stochastic integrals (60H05)

Related Items

On the persistent homology of almost surely \(C^0\) stochastic processes ⋮ Malliavin calculus and rough paths ⋮ The play operator, the truncated variation and the generalisation of the Jordan decomposition ⋮ Densities for rough differential equations under Hörmander's condition ⋮ Self-similar real trees defined as fixed points and their geometric properties ⋮ Representation Formulae for the Fractional Brownian Motion ⋮ Integrability and concentration of the truncated variation for the sample paths of fractional Brownian motions, diffusions and Lévy processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local independence of fractional Brownian motion
• Rayleigh processes, real trees, and root growth with re-grafting
• Brownian excursions, stochastic integrals, and representation of Wiener functionals
• Curvilinear integrals along enriched paths
• Differential equations driven by rough paths. Ecole d'Eté de Probabilités de Saint-Flour XXXIV -- 2004. Lectures given at the 34th probability summer school, July 6--24, 2004.
• The strong p-variation of martingales and orthogonal series
• Subdiffusive behavior of random walk on a random cluster
• Brownian excursions, trees and measure-valued branching processes
• Integration with respect to fractal functions and stochastic calculus. I
• Differential equations driven by rough signals
• Branching processes in Lévy processes: The exploration process
• Forward, backward and symmetric stochastic integration
• Quadratic variations and estimation of the local Hölder index of a Gaussian process
• Probabilistic and fractal aspects of Lévy trees
• Maximum of a fractional Brownian motion: Probabilities of small values
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Controlling rough paths
• Limit theorems for logarithmic averages of fractional Brownian motions
• The continuum random tree. III
• Probability and real trees. Ecole d'Eté de Probabilités de Saint-Flour XXXV -- 2005. Lecture given at the Saint-Flour probability summer school, July 6--23, 2005.
• \(m\)-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• An inequality of the Hölder type, connected with Stieltjes integration
• System Control and Rough Paths
• Path-wise solutions of stochastic differential equations driven by Lévy processes

This page was built for publication: A tree approach to \(p\)-variation and to integration